The Shear Modulus of Liquid Foam

Abstract

A strain energy function for liquid foam is formulated by modeling foam as a collection of randomly oriented surfaces with surface tension on the faces. The surfaces are assumed to follow the mean strain. It is assumed that surface forces equilibriate between neighboring elements and hence that the value of surface tension γ is the same on all faces and a function of total surface area. In particular, an expansion of the strain energy function in powers of the strain is used to obtain the value for the shear modulus in the linear elasticity approximation. The predicted value of the shear modulus is 4/15 γS/ V where S/ V is the surface to volume ratio or 2/5 ΔP, where ΔP is the overpressure of the gas trapped in the foam. In rheometric tests, foam was found to behave as a viscoelastic material. The shear modulus that describes the initial elastic response was found to be about 84 percent of the predicted value.